There is a school of thought that says we should change how we use the English language. This school thinks that the proper way to speak is to assume non-binary until informed otherwise and that appealing to "what sounds right" or "the rules of grammar" is unacceptable linguistic conservativism.
I am not making that argument. I'm just raising it because it seems relevant here. I would point out that, even if you disagree with this argument, it seems reasonable to think that people should be able to choose how they use pronouns, whether their usage flies in the face of linguistic convention/rules of grammar or goes along with them.
That said, precisely because communication is a mutual endeavour, and language is a coöperative framework, there is no guarantee that -- just because you choose to use "they" in this way -- others will follow. I wouldn't be terribly surprised if, within a generation, "they" became an unmarked definite gender-neutral pronoun in English (today it is arguably unmarked in the case of an indefinite antecedent, but extremely marked otherwise). But I wouldn't be terribly surprised if it didn't, either. Language change is an emergent process and not something that can easily be forced in either conservative or radical directions.